分数与指数的运算

分数与指数的运算
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2024-10-16 17:46
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本范例演示了如何分数与指数的运算,展示了分数与指数的关系。核心数学概念包括指数的定义、指数的运算规则以及分数与指数的关系。作图要点包括使用 GeoGebra 的 Textfield、Shuffle、If、Join、Polygon 等命令和对象。适合的学段或用途包括初中数学教育,特别是 7-8 年级的学生。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2, 3}) → ModusList, {2, 3, 1}
  4. If(questionCount ≥ 4, 4, questionCount) → metaprogression
  5. Join({{1}, ModusList}) → ModusMioPlaylist
  6. Shuffle(Sequence[i, i, 1, 19]) → AStartList, {15, 19, 5, 14, 2, 17, 10, 11, 6, 4, 12, 7, 9, 1, 3, 8, 13, 18, 16}
  7. Shuffle(Sequence[i, i, 1, 19]) → BStartList, {3, 1, 9, 18, 19, 6, 10, 2, 15, 14, 5, 11, 8, 17, 7, 12, 13, 16, 4}
  8. Shuffle(Sequence[i, i, 1, 9]) → AMidList, {7, 6, 9, 8, 5, 3, 2, 1, 4}
  9. Shuffle(Sequence[i, i, 1, 9]) → BMidList, {1, 5, 7, 9, 2, 6, 4, 8, 3}
  10. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {1, 8, 6, 8, 1, 10, 5, 7, 3, 7, 0, 0, 4, 4, 5, 2, 6, 10, 4, 5, 3, 0, 4, 9, 1, 0, 6, 9, 4, 9, 9, 6, 6, 8, 7, 6, 9, 5, 1, 6, 4, 4, 3, 9, 0, 5, 6, 5, 0, 1, 3, 5, 1, 1, 6, 8, 1, 5, 9, 1, 7, 3, 9, 0, 9, 6, 3, 7, 8, 10, 2, 5, 0, 8, 7, 2, 8, 0, 5, 3, 5, 1, 4, 1, 5, 2, 10, 8, 0, 0, 7, 0, 10, 0, 8, 2, 4, 0, 2, 3}
  12. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 5, 3, 9, 1, 5, 6, 8, 0, 7, 3, 2, 7, 7, 1, 9, 7, 6, 4, 9, 7, 6, 6, 2, 8, 7, 1, 8, 3, 8, 9, 0, 6, 7, 3, 3, 5, 5, 9, 8, 4, 7, 1, 2, 7, 10, 4, 6, 6, 1, 0, 9, 1, 4, 8, 4, 4, 7, 10, 10, 1, 9, 0, 3, 4, 7, 8, 10, 4, 6, 2, 2, 10, 1, 1, 9, 2, 2, 1, 7, 4, 0, 3, 3, 8, 3, 8, 0, 2, 8, 10, 0, 8, 2, 10, 7, 3, 0, 0, 3}
  14. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  15. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  16. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  17. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  18. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  19. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  20. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  21. Shuffle(Sequence[i, i, -10, 10] \ {0}) → XGanzzhahlList, {6, -2, -3, 1, 4, 8, 3, 10, -10, 2, 9, -1, -6, -8, -4, 5, 7, -7, -9, -5}
  22. Shuffle(Sequence[i, i, 1, 10]) → XStartList, {8, 9, 4, 2, 10, 1, 5, 7, 3, 6}
  23. Shuffle(Join[{XDezizahlList, XGanzzhahlList}]) → XMidList, {-9, 1, -0.4, -0.8, 3, 5, 3.5, -1.5, 2, 1.1, 3.8, 0.4, 0.7, 0.9, 1.8, 1.2, 10, 4.6, -2, 0.6, 8, -1.3, 0.3, -7, 2.5, 3.6, 4.1, 4, -4, 2.4, 0.2, 2.9, 4.3, -0.1, 2.8, -1.9, 4.5, -0.3, -0.5, -6, 3.3, 3.9, -1.2, 4.4, 1.6, -5, -0.7, 0.1, -0.9, 3.2, -3, 4.8, -8, 1.3, 5, -1.1, 4.9, 4, -1.7, 0.5, 4.7, 1.4, -0.6, 1.5, 3.7, 3, -1.6, 1.7, 2.3, -1, 2.1, -1.8, -0.2, -2, 9, 6, 4.2, -10, 2, -1.4, 3.1, 2.6, 0.8, 7, 2.2, 3.4, -1, 1.9, 2.7, 1}
  24. Text(Text2, E, false, true, -1, 0) → Text6
  25. Text(Text3, F, false, true, -1, 0) → Text7
  26. Midpoint(Corner[Text6, 1], Corner[Text6, 4]) → Pos1
  27. Midpoint(Corner[Text7, 1], Corner[Text7, 3]) → Pos2
  28. Textfield(input3) → InputBox3
  29. Text(Text4, B, false, true, -1, 0) → Text10
  30. Midpoint(Corner[Text10, 1], Corner[Text10, 3]) → Pos3
  31. If(modus ≟ 1, Defined[input1], modus ≟ 2, Defined[input2], Defined[input3]) → fixed
  32. Midpoint(Corner[Text12, 1], Corner[Text12, 3]) → Pos4
  33. Text(Text12, A, false, true, -1, 0) → Text5

AI 绘图提示语参考

画一个展示幂次除法关系的图形,包含两个输入框用于输入数值,通过随机生成的序列和坐标点绘制几何图形,展示分数与指数的关系,并用几何形状表示计算结果,整体构造顺序从输入到输出逐步展示幂次运算的规则。
以上提示语为根据原始绘图命令整理而来,仅供参考。